Answer :

Formula used


Isosceles triangle property


If 2 angles of triangle are equal then their corresponding sides are also equal


Perpendicular drawn through tangent pass through centre


Solution



In Δ QPO


QOP = 90°


By angle sum property


QOP + QPO + OQP = 180°


QPO = 90° - OQP


In Δ QOR


As OQ = OR radius of same circle


OQP = ORP


As RS is tangent


ORS = 90°


In Δ SPR


SPR = OPQ (Vertically opposite angles)


SPR = 90° - OQP


SRP = ORS - ORP


= 90° - OQP


Hence;


SPR = SRP


By isosceles triangle property


SR = SP


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